{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "袁可潞和杨雨凤的期中作业"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np # 数据处理最重要的模块\n",
    "import pandas as pd # 数据处理最重要的模块\n",
    "import scipy.stats as stats # 统计模块\n",
    "import scipy\n",
    "# import pymysql  # 导入数据库模块\n",
    "\n",
    "from datetime import datetime # 时间模块\n",
    "import statsmodels.formula.api as smf  # OLS regression\n",
    "\n",
    "# import pyreadr # read RDS file\n",
    "\n",
    "from matplotlib import style\n",
    "import matplotlib.pyplot as plt  # 画图模块\n",
    "import matplotlib.dates as mdates\n",
    "\n",
    "\n",
    "from matplotlib.font_manager import FontProperties # 作图中文\n",
    "from pylab import mpl\n",
    "#mpl.rcParams['font.sans-serif'] = ['SimHei']\n",
    "#plt.rcParams['font.family'] = 'Times New Roman'\n",
    "\n",
    "\n",
    "#输出矢量图 渲染矢量图\n",
    "%matplotlib inline\n",
    "%config InlineBackend.figure_format = 'svg'\n",
    "\n",
    "from IPython.core.interactiveshell import InteractiveShell # jupyter运行输出的模块\n",
    "#显示每一个运行结果\n",
    "InteractiveShell.ast_node_interactivity = 'all'\n",
    "\n",
    "#设置行不限制数量\n",
    "#pd.set_option('display.max_rows',None)\n",
    "\n",
    "#设置列不限制数量\n",
    "pd.set_option('display.max_columns', None)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 中国股票市场收益率（月度）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Raw_return</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>month</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>2003-02-28</th>\n",
       "      <td>0.008074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-03-31</th>\n",
       "      <td>-0.000893</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-04-30</th>\n",
       "      <td>0.007189</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-05-31</th>\n",
       "      <td>0.036032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2003-06-30</th>\n",
       "      <td>-0.057249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>-0.032849</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.173908</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>260 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            Raw_return\n",
       "month                 \n",
       "2003-02-28    0.008074\n",
       "2003-03-31   -0.000893\n",
       "2003-04-30    0.007189\n",
       "2003-05-31    0.036032\n",
       "2003-06-30   -0.057249\n",
       "...                ...\n",
       "2024-05-31   -0.005801\n",
       "2024-06-30   -0.038684\n",
       "2024-07-31   -0.009656\n",
       "2024-08-31   -0.032849\n",
       "2024-09-30    0.173908\n",
       "\n",
       "[260 rows x 1 columns]"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_csv('C:/Users/21230/Desktop/Python-homework/000001.csv')\n",
    "data['Day'] = pd.to_datetime(data['Day'],format='%Y/%m/%d')\n",
    "data.set_index('Day', inplace = True)\n",
    "data_new = data['2003-02':'2024-09'].copy()\n",
    "data_new['Close'] = pd.to_numeric(data_new['Close'])\n",
    "data_new['Preclose'] = pd.to_numeric(data_new['Preclose'])\n",
    "data_new['Raw_return'] = data_new['Close'] / data_new['Preclose'] - 1\n",
    "Month_data = data_new.resample('M')['Raw_return'].apply(lambda x: (1+x).prod() - 1).to_frame()\n",
    "Month_data.reset_index(inplace = True)\n",
    "Month_data.rename(columns = {'Day':'month'}, inplace = True)\n",
    "Month_data.set_index('month', inplace = True)\n",
    "Month_data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 描述性统计"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 基础描述"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "count    260.000000\n",
       "mean       0.005679\n",
       "std        0.071905\n",
       "min       -0.246314\n",
       "25%       -0.033529\n",
       "50%        0.004463\n",
       "75%        0.042564\n",
       "max        0.274464\n",
       "Name: Raw_return, dtype: float64"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Month_data['Raw_return'].describe()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "均值0.0057 标准差是0.07\n",
    "- 第一组 -0.25<=R<=-0.036\n",
    "- 第二组 -0.036<R<=0.004\n",
    "- 第三组 -0.004<R<=0.043\n",
    "- 第四组 -0.043<R<=0.274"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 具体均值"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "\\bar{R}=\\frac{\\sum(R)}{N}\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.005679475706172382"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(Month_data['Raw_return'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 偏度 skewness"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "s=\\frac{1}{N} \\sum^{N}_{i=1} [(\\frac{R-\\bar{R}}{\\sigma}^3)]\n",
    "$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.5248051701197491"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(data_new[data_new['Raw_return'] > 0]) / len(data_new)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
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      "text/plain": [
       "<Figure size 1200x600 with 1 Axes>"
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     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize = (12,6))\n",
    "\n",
    "ax.plot('Raw_return', # 图片数据\n",
    "'*-', # 图片类型,\n",
    "color = 'r', # 图片颜色\n",
    "label = 'Monthly Return', # 图片标签\n",
    "linewidth = 1, # 图片线宽\n",
    "data = Month_data) # 图片数据来源\n",
    "ax.set_title(\"China's stock market\") # 图片标题\n",
    "ax.set_ylabel('Return') # 图片y轴标签\n",
    "ax.set_xlabel('Year') # 图片x轴标签\n",
    "\n",
    "# 设置x轴的日期显示格式\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax.xaxis.set_major_formatter(data_format)\n",
    "ax.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "# 转置x轴的日期显示格式\n",
    "plt.xticks(rotation = 90)\n",
    "\n",
    "# 添加图例\n",
    "plt.legend(loc='upper right',fontsize = 8)\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 中国进出口额（月度）"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
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       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>TotExpImp_Mon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-31</th>\n",
       "      <td>54.0700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-02-28</th>\n",
       "      <td>67.7700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-03-31</th>\n",
       "      <td>85.7700</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-04-30</th>\n",
       "      <td>91.0600</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-05-31</th>\n",
       "      <td>95.4100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>5217.9227</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>5161.4875</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>5160.3153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>5260.9601</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>5257.1375</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>417 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            TotExpImp_Mon\n",
       "Date                     \n",
       "1990-01-31        54.0700\n",
       "1990-02-28        67.7700\n",
       "1990-03-31        85.7700\n",
       "1990-04-30        91.0600\n",
       "1990-05-31        95.4100\n",
       "...                   ...\n",
       "2024-05-31      5217.9227\n",
       "2024-06-30      5161.4875\n",
       "2024-07-31      5160.3153\n",
       "2024-08-31      5260.9601\n",
       "2024-09-30      5257.1375\n",
       "\n",
       "[417 rows x 1 columns]"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "teim=pd.read_csv('C:/Users/21230/Desktop/Python-homework/RESSET_MACHINAIMPEXP_1.csv')\n",
    "teim['Date']=pd.to_datetime(teim['Date'])\n",
    "teim.set_index('Date',inplace=True)\n",
    "teim.sort_values(by = ['Date'],axis=0, ascending=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 理论论述 Theory Motivation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "- 为什么选用中国月度进出口额来回归预测中国月度股票收益率：\n",
    "\n",
    "首先，进出口额反映经济的状况，进出口额是衡量一个国家对外贸易活动的重要指标之一，也是评估一个国家经济发展水平的重要标志。月度进出口额数据可以反映一个国家在一定时期内的经济活跃度和对外开放程度。当进出口额增加时，通常意味着该国的经济活动较为繁荣，经济增长势头良好。其次，经济状况与股票收益率的关系。经济状况是影响股票收益率的重要因素之一。当经济繁荣时，企业盈利能力增强，股票市场的整体表现通常也会较好。此时，投资者对股票市场的信心增强，愿意投入更多的资金，从而推动股票价格上涨，提高股票收益率。然后，进出口额作为预测因子的可行性。基于上述两点，可以看出进出口额与股票收益率之间存在一定的正相关关系。因此，可以将月度进出口额作为预测中国月度股票收益率的一个因子。通过回归分析等方法，可以建立预测模型，利用历史数据来预测未来的股票收益率。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 数据归一化处理"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "X_{normalized}=\\frac{X-min(X)}{max(X)-min(X)}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "为了将数据转换为统一的范围，首先对数据进行归一化处理，从而便于分析和比较"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "      <th></th>\n",
       "      <th>TotExpImp_Mon</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1990-01-31</th>\n",
       "      <td>0.000000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-02-28</th>\n",
       "      <td>0.002359</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-03-31</th>\n",
       "      <td>0.005459</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-04-30</th>\n",
       "      <td>0.006370</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1990-05-31</th>\n",
       "      <td>0.007119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>0.889232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>0.879513</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>0.879312</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-08-31</th>\n",
       "      <td>0.896643</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-09-30</th>\n",
       "      <td>0.895985</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>417 rows × 1 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            TotExpImp_Mon\n",
       "Date                     \n",
       "1990-01-31       0.000000\n",
       "1990-02-28       0.002359\n",
       "1990-03-31       0.005459\n",
       "1990-04-30       0.006370\n",
       "1990-05-31       0.007119\n",
       "...                   ...\n",
       "2024-05-31       0.889232\n",
       "2024-06-30       0.879513\n",
       "2024-07-31       0.879312\n",
       "2024-08-31       0.896643\n",
       "2024-09-30       0.895985\n",
       "\n",
       "[417 rows x 1 columns]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "teim['TotExpImp_Mon']=pd.to_numeric(teim['TotExpImp_Mon'])\n",
    "teim_min=np.min(teim)\n",
    "teim_max=np.max(teim)\n",
    "normalized_teim=teim.resample('D')['TotExpImp_Mon'].apply(lambda x:(x-teim_min)/(teim_max-teim_min)).to_frame()\n",
    "normalized_teim"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 预测变量和收益率图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "    <tr>\n",
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       "      <td>...</td>\n",
       "      <td>...</td>\n",
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       "    <tr>\n",
       "      <th>2024-05-31</th>\n",
       "      <td>-0.005801</td>\n",
       "      <td>0.871132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2024-06-30</th>\n",
       "      <td>-0.038684</td>\n",
       "      <td>0.889232</td>\n",
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       "    <tr>\n",
       "      <th>2024-07-31</th>\n",
       "      <td>-0.009656</td>\n",
       "      <td>0.879513</td>\n",
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       "      <th>2024-08-31</th>\n",
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       "      <th>2024-09-30</th>\n",
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       "      <td>0.896643</td>\n",
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       "            Raw_return  TotExpImp_Mon\n",
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       "2003-03-31   -0.000893       0.073752\n",
       "2003-04-30    0.007189       0.102002\n",
       "2003-05-31    0.036032       0.111607\n",
       "2003-06-30   -0.057249       0.103390\n",
       "...                ...            ...\n",
       "2024-05-31   -0.005801       0.871132\n",
       "2024-06-30   -0.038684       0.889232\n",
       "2024-07-31   -0.009656       0.879513\n",
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       "2024-09-30    0.173908       0.896643\n",
       "\n",
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     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
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   ],
   "source": [
    "month_end_dates=teim.index+pd.offsets.MonthEnd(1)\n",
    "normalized_teim.index=month_end_dates\n",
    "reg_data = pd.merge(Month_data, normalized_teim, left_index=True, right_index=True)\n",
    "reg_data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
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      "text/plain": [
       "<Figure size 1500x600 with 2 Axes>"
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   ],
   "source": [
    "fig, ax1 = plt.subplots(figsize=(15,6))\n",
    "# the linewidth and marker size are set to be very small\n",
    "ax1.plot(Month_data['Raw_return'],color='r',marker='*',linewidth=0.9,\n",
    "         markersize=4,\n",
    "         linestyle='--',label='China Stock Market Return')\n",
    "ax1.set_ylabel('China Stock Market Return',color='c')\n",
    "#ax1.set_xlabel('Month')\n",
    "\n",
    "# 设置x轴的日期显示格式\n",
    "data_format = mdates.DateFormatter('%Y')\n",
    "ax1.xaxis.set_major_formatter(data_format)\n",
    "ax1.xaxis.set_major_locator(mdates.YearLocator())\n",
    "\n",
    "# 转置x轴的日期显示格式\n",
    "plt.xticks(rotation = 90)\n",
    "\n",
    "ax2 = ax1.twinx()\n",
    "ax2.plot(reg_data['TotExpImp_Mon'].shift(2),color='blue',marker='.',linewidth=0.9,\n",
    "         markersize=4,\n",
    "         linestyle='--',label='TotExpImp_Mon')\n",
    "\n",
    "ax2.set_ylabel('TotExpImp_Mon',color='r')\n",
    "\n",
    "plt.title('China Stock Market Return and TotExpImp_Mon')\n",
    "\n",
    "# change the legend into one box\n",
    "lines, labels = ax1.get_legend_handles_labels()\n",
    "lines2, labels2 = ax2.get_legend_handles_labels()\n",
    "ax2.legend(lines + lines2, labels + labels2, loc='upper left')\n",
    "\n",
    "# save figure\n",
    "\n",
    "plt.show();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$\n",
    "R_{t+1}=\\alpha+\\beta*TEIM_{t-1}+\\epsilon_t\n",
    "$$\n",
    "\n",
    "- 原假设 $ \\beta_0=0 $\n",
    "- 备择假设 $\\beta_1 \\neq 0 $"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 预测回归"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 全样本 Full-Sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.003\n",
      "Model:                            OLS   Adj. R-squared:                 -0.001\n",
      "Method:                 Least Squares   F-statistic:                    0.5394\n",
      "Date:                Tue, 26 Nov 2024   Prob (F-statistic):              0.463\n",
      "Time:                        20:37:31   Log-Likelihood:                 296.72\n",
      "No. Observations:                 246   AIC:                            -589.4\n",
      "Df Residuals:                     244   BIC:                            -582.4\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "=================================================================================\n",
      "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------\n",
      "Intercept         0.0143      0.016      0.890      0.373      -0.017       0.046\n",
      "TotExpImp_Mon    -1.7688      2.408     -0.734      0.463      -6.489       2.952\n",
      "==============================================================================\n",
      "Omnibus:                       15.691   Durbin-Watson:                   1.740\n",
      "Prob(Omnibus):                  0.000   Jarque-Bera (JB):               40.142\n",
      "Skew:                          -0.170   Prob(JB):                     1.92e-09\n",
      "Kurtosis:                       4.949   Cond. No.                         445.\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n"
     ]
    }
   ],
   "source": [
    "reg_data['TotExpImp_Mon'] = reg_data['TotExpImp_Mon'].shift(2)/100\n",
    "model_teim = smf.ols('Raw_return ~ TotExpImp_Mon',\n",
    "                 data=reg_data['2003-02':'2023-09']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_teim.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "-对回归模型进行文字描述，主要包括系数、标准误差、z值、P值、R方\n",
    " \n",
    " 系数分析：系数为-146.9653，这表明在其他条件不变的情况下，TEIM每增加1个单位，股票收益率将平均减少146.9653个单位。这个负系数暗示了TEIM与股票收益率之间存在负相关关系，即TEIM的增加可能会导致股票收益率的下降。\n",
    "\n",
    "P值分析：P值为0.551，这个值大于常用的显著性水平0.05。在统计学中，如果P值大于0.05，我们通常认为结果不具有统计显著性，即没有足够的证据拒绝原假设。这里的原假设可能是TEIM与股票收益率之间没有关系。因此，我们接受原假设，认为TEIM对股票收益率的影响不显著。\n",
    "\n",
    "R方值分析：R方（R-squared）值为0.002，这表示模型中解释变量（TEIM）只能解释股票收益率变动的2%。这是一个非常低的值，表明模型的解释能力非常有限，拟合程度较低。这可能意味着模型中遗漏了一些重要的变量，这些变量可能对股票收益率有更大的影响。\n",
    "\n",
    "调整后的R方值分析：调整后的R方值为-0.002，这比R方值还要低，表明在考虑自由度后，模型的拟合度不仅没有改善，反而变得更差。调整后的R方值考虑了模型中解释变量的数量，当模型中包含的变量过多时，即使R方值增加，调整后的R方值也可能减少，因为它会惩罚过度拟合。这里的负值表明模型的预测能力非常差，甚至不如一个简单的截距模型。\n",
    " "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 子样本 Sub-Sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "reg_data_1=reg_data['2020':'2023']"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "                            OLS Regression Results                            \n",
      "==============================================================================\n",
      "Dep. Variable:             Raw_return   R-squared:                       0.027\n",
      "Model:                            OLS   Adj. R-squared:                  0.004\n",
      "Method:                 Least Squares   F-statistic:                    0.7813\n",
      "Date:                Tue, 26 Nov 2024   Prob (F-statistic):              0.382\n",
      "Time:                        20:37:31   Log-Likelihood:                 75.711\n",
      "No. Observations:                  43   AIC:                            -147.4\n",
      "Df Residuals:                      41   BIC:                            -143.9\n",
      "Df Model:                           1                                         \n",
      "Covariance Type:                  HAC                                         \n",
      "=================================================================================\n",
      "                    coef    std err          z      P>|z|      [0.025      0.975]\n",
      "---------------------------------------------------------------------------------\n",
      "Intercept         0.0444      0.048      0.921      0.357      -0.050       0.139\n",
      "TotExpImp_Mon  -524.8900    593.811     -0.884      0.377   -1688.738     638.958\n",
      "==============================================================================\n",
      "Omnibus:                        0.616   Durbin-Watson:                   2.201\n",
      "Prob(Omnibus):                  0.735   Jarque-Bera (JB):                0.726\n",
      "Skew:                           0.167   Prob(JB):                        0.696\n",
      "Kurtosis:                       2.458   Cond. No.                     7.54e+04\n",
      "==============================================================================\n",
      "\n",
      "Notes:\n",
      "[1] Standard Errors are heteroscedasticity and autocorrelation robust (HAC) using 6 lags and without small sample correction\n",
      "[2] The condition number is large, 7.54e+04. This might indicate that there are\n",
      "strong multicollinearity or other numerical problems.\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\21230\\AppData\\Local\\Temp\\ipykernel_1236\\1229646428.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  reg_data_1['TotExpImp_Mon'] = reg_data_1['TotExpImp_Mon'].shift(2)/100\n"
     ]
    }
   ],
   "source": [
    "reg_data_1['TotExpImp_Mon'] = reg_data_1['TotExpImp_Mon'].shift(2)/100\n",
    "model_teim = smf.ols('Raw_return ~ TotExpImp_Mon',\n",
    "                 data=reg_data_1['2003-02':'2023-09']).fit(\n",
    "                     cov_type='HAC', cov_kwds={'maxlags': 6})\n",
    "print(model_teim.summary())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    " 系数分析：系数为-1.331e+04，这表明在其他条件不变的情况下，TEIM每增加1个单位，股票收益率将平均减少13,310个单位。这个负系数暗示了TEIM与股票收益率之间存在负相关关系，即TEIM的增加可能会导致股票收益率的显著下降。\n",
    "\n",
    "P值分析：P值为0.640，这个值大于常用的显著性水平0.05。在统计学中，如果P值大于0.05，我们通常认为结果不具有统计显著性，即没有足够的证据拒绝原假设。这里的原假设可能是TEIM与股票收益率之间没有关系。因此，我们接受原假设，认为TEIM对股票收益率的影响不显著。\n",
    "\n",
    "R方值分析：R方（R-squared）值为0.002，这表示模型中解释变量（TEIM）只能解释股票收益率变动的0.2%。这是一个非常低的值，表明模型的解释能力非常有限，拟合程度较低。这可能意味着模型中遗漏了一些重要的变量，这些变量可能对股票收益率有更大的影响。\n",
    "\n",
    "调整后的R方值分析：调整后的R方值为-0.023，这比R方值还要低，表明在考虑自由度后，模型的拟合度不仅没有改善，反而变得更差。调整后的R方值考虑了模型中解释变量的数量，当模型中包含的变量过多时，即使R方值增加，调整后的R方值也可能减少，因为它会惩罚过度拟合。这里的负值表明模型的预测能力非常差，甚至不如一个简单的截距模型。"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 整理结果"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 分析与理论论述不一致的原因"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "1.影响股票收益率的多元性：股票收益率的变化受到多种宏观经济因素和微观市场因素的影响。除了进出口额之外，还包括经济增长率、通货膨胀率、利率、汇率、政策变化、市场情绪、投资者预期等。这些因素相互作用，共同决定了股票市场的走势和股票收益率的变化。因此，仅仅依靠月度进出口额来预测股票收益率是片面的，可能会忽略其他重要的影响因素。\n",
    "\n",
    "2.进出口额与股票收益率关系的复杂性：虽然进出口额与股票收益率之间存在一定的正相关关系，但这种关系并不是绝对的。在不同的经济周期和市场环境下，进出口额对股票收益率的影响可能存在差异。此外，进出口额的结构和质量也会对股票收益率产生影响。\n",
    "\n",
    "3.预测模型的局限性和不确定性：任何预测模型都存在局限性和不确定性。月度进出口额数据本身可能受到多种因素的影响，如季节性因素、统计误差等，这些因素可能导致数据波动和不稳定。此外，预测模型本身也可能存在偏差和误差，如模型设定不合理、参数选择不当等。因此，即使建立了基于月度进出口额的预测模型，其预测结果也可能存在较大的不确定性和误差。"
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